I'm sure a lot of us already know about this wonderful piece of software. But for those of us who don't, I cannot recommend more that you investigate FL Studio if you are interested in composing on a computer.
There is a demo version which is free, and the only limitation as far as I know is the fact that you can't save your projects to edit later, however you can compile them into mp3/wav/mid. The full program costs $50, which is amazing for such a feature-rich program.
The only thing I don't like about it is that when you convert channels for midi output, it is rather difficult to edit them later as no sound is played with converted channels.
Overall, it is a great way to introduce yourself to electronic music composing and after using it for the past 6 months I have been thoroughly impressed.
Download: http://flstudio.image-line.com
Happy composing!